{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weak Galerkin Methods for Poisson Equation in 3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is to show the rate of convergence of the linear finite element approximation of the Poisson equation on the unit cube:\n",
    "\n",
    "$$- \\Delta u = f \\; \\hbox{in } (0,1)^3$$\n",
    "\n",
    "for the following boundary conditions\n",
    "- Non-empty Dirichlet boundary condition: $u=g_D \\hbox{ on }\\Gamma_D, \\nabla u\\cdot n=g_N \\hbox{ on }\\Gamma_N.$\n",
    "- Pure Neumann boundary condition: $\\nabla u\\cdot n=g_N \\hbox{ on } \\partial \\Omega$.\n",
    "- Robin boundary condition: $g_R u + \\nabla u\\cdot n=g_N \\hbox{ on }\\partial \\Omega$.\n",
    "\n",
    "**References**:\n",
    "- [Quick Introduction to Finite Element Methods](femdoc.html)\n",
    "- [Introduction to Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch2FEM.pdf)\n",
    "- [Progamming of Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch3FEMCode.pdf)\n",
    "\n",
    "**Subroutines**:\n",
    "\n",
    "    - Poisson3WG\n",
    "    - cubePoisson3WG\n",
    "    - femPoisson3\n",
    "    - Poisson3WGfemrate\n",
    "    \n",
    "The method is implemented in `Poisson3` subroutine and tested in `cubePoisson`. Together with other elements (P1, P2,Q1,WG), `femPoisson3` provides a concise interface to solve Poisson equation. The P1 element is tested in `Poisson3femrate`. This doc is based on `Poisson3femrate`.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Lowest Order Weak Galerkin Element\n",
    "\n",
    "The basis and the local matrices can be found in [Progamming of Weak Galerkin Methods](http://www.math.uci.edu/~chenlong/ifemdoc/fem/WGprogramming.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixed boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%% Setting\n",
    "[node,elem] = cubemesh([0,1,0,1,0,1],0.5); \n",
    "mesh = struct('node',node,'elem',elem);\n",
    "option.L0 = 1;\n",
    "option.maxIt = 4;\n",
    "option.elemType = 'WG';\n",
    "option.printlevel = 1;\n",
    "option.plotflag = 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     6528,  #nnz:    25576, smoothing: (1,1), iter: 17,   err = 7.80e-09,   time = 0.14 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    50688,  #nnz:   223244, smoothing: (1,1), iter: 17,   err = 9.10e-09,   time = 0.28 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   399360,  #nnz:  1815764, smoothing: (1,1), iter: 17,   err = 9.78e-09,   time =  2.6 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   864   2.500e-01   1.62586e-02   5.82293e-01   2.08771e-01   2.74409e-02\n",
      "  6528   1.250e-01   4.03120e-03   2.94275e-01   9.83063e-02   7.18140e-03\n",
      " 50688   6.250e-02   1.00634e-03   1.47521e-01   4.83526e-02   1.81988e-03\n",
      "399360   3.125e-02   2.51527e-04   7.38079e-02   2.40757e-02   4.58839e-04\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   864   1.70e-01   9.68e-03   9.00e-02   1.00e-02\n",
      "  6528   1.10e-01   1.39e-01   4.00e-02   2.00e-02\n",
      " 50688   4.10e-01   2.82e-01   2.00e-01   9.00e-02\n",
      "399360   4.14e+00   2.59e+00   1.77e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
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3T3/6k1EKLAQRNejkPCJ9Qcrcph/Zs2P6mt8NN+qoIP/c1D67iis049yyITyC8IkSwABA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\nEKAgIQiC/P9GwaAAANfA0EmIwbn2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2bNi9e3c+nz948KDzgMOHD+fz+S9cMz09Hf0ggYjVboWkVja+9zJ9hzTXIkkf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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Non-empty Dirichlet boundary condition.\n",
    "pde = sincosdata3;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Dirichlet','~(x==0)','Neumann','x==0');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pure Neumann boundary condition\n",
    "\n",
    "When pure Neumann boundary condition is posed, i.e., $-\\Delta u =f$ in $\\Omega$ and $\\nabla u\\cdot n=g_N$ on $\\partial \\Omega$, the data should be consisitent in the sense that $\\int_{\\Omega} f \\, dx + \\int_{\\partial \\Omega} g \\, ds = 0$. The solution is unique up to a constant. A post-process is applied such that the constraint $\\int_{\\Omega}u_h dx = 0$ is imposed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     6528,  #nnz:    27909, smoothing: (1,1), iter: 20,   err = 7.29e-09,   time =  0.1 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    50688,  #nnz:   232473, smoothing: (1,1), iter: 21,   err = 4.09e-09,   time = 0.33 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   399360,  #nnz:  1858773, smoothing: (1,1), iter: 22,   err = 4.23e-09,   time =  3.2 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   864   2.500e-01   2.14311e-02   5.83747e-01   2.58148e-01   1.21000e-01\n",
      "  6528   1.250e-01   5.28526e-03   2.94315e-01   1.08333e-01   3.88004e-02\n",
      " 50688   6.250e-02   1.31642e-03   1.47495e-01   4.97809e-02   1.03134e-02\n",
      "399360   3.125e-02   3.28925e-04   7.38022e-02   2.42593e-02   2.61798e-03\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   864   6.00e-02   2.09e-03   2.00e-02   0.00e+00\n",
      "  6528   3.00e-02   1.01e-01   3.00e-02   1.00e-02\n",
      " 50688   3.90e-01   3.27e-01   1.60e-01   8.00e-02\n",
      "399360   4.20e+00   3.25e+00   1.62e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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29l69erXNh27fvt26det///vfNE0fO3bM29v7yJEjNE2vWLHi0KFDNE2XlZUF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\ngBPQhwQAAJyAggQAAJyAggQAAJzwL3ViJXtrfSLXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Neumann boundary condition.\n",
    "option.plotflag = 0;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Neumann');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robin boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     6528,  #nnz:    27912, smoothing: (1,1), iter: 17,   err = 3.75e-09,   time = 0.085 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    50688,  #nnz:   232476, smoothing: (1,1), iter: 17,   err = 7.36e-09,   time = 0.26 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   399360,  #nnz:  1858776, smoothing: (1,1), iter: 17,   err = 7.33e-09,   time =  2.1 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   864   2.500e-01   2.06220e-02   5.78283e-01   2.29477e-01   5.01643e-02\n",
      "  6528   1.250e-01   5.16104e-03   2.93750e-01   1.01338e-01   1.36257e-02\n",
      " 50688   6.250e-02   1.29034e-03   1.47454e-01   4.87501e-02   3.60385e-03\n",
      "399360   3.125e-02   3.22587e-04   7.37995e-02   2.41260e-02   9.11692e-04\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   864   4.00e-02   1.77e-03   1.00e-02   0.00e+00\n",
      "  6528   6.00e-02   8.46e-02   3.00e-02   1.00e-02\n",
      " 50688   3.00e-01   2.61e-01   1.80e-01   1.20e-01\n",
      "399360   3.01e+00   2.15e+00   1.72e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
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dMWNG165dmawEBgsRAJDJZAEBASJUI4Y4XU6HVEvyDGl06qUFUOl2RkdECS0Z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\nRQSCUgkUZWaKyGUnk1CQEDHgijEO69atW79+PXO6e/fuYcO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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Robin boundary condition.\n",
    "pde = sincosRobindata3;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Robin');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "The optimal rate of convergence of the H1-norm (1st order) and L2-norm\n",
    "(2nd order) is observed. No superconvergence for $\\|\\nabla u_I - \\nabla u_h\\|$.\n",
    "\n",
    "MGCG converges uniformly in all cases."
   ]
  }
 ],
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     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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